J. KHEINBERG ON THE BLACK AND WHITE DOT PHENOMENON. 115 



a diatom which is studded with perforations, in other words with 

 vertical partitions, we get an immense number of the bands 

 parallel to each other in each of the two directions, forming a 

 sort of trellis-work of light and darkness (Fig. 7). And as 

 sections of trellis-work taken one below the other would show 

 alternately light and dark spaces, so do the diatoms when the 

 focus is adjusted to different planes. One great point must here 

 be borne in mind. We cannot really see any plane of the 

 diatom below that of its upper surface, although we may slightly 

 rack down the objective. Imagine for a moment a perfectly 

 free space below the upper surface of the diatom. Then if the 

 objective were racked down we should simply see the state of 

 light into which the rays proceeding upwards from the upper 

 surface of the diatom would form themselves, if they were 

 continued downwards as far as the plane on which the objective 

 is focussed. And that is precisely what we see, although the 

 diatom has not been removed. In like manner, if we rack 

 the objective up so as to focus on a slightly higher plane than 

 the surface of the diatom, we may still see markings, though 

 they are fictitious and merely represent the result in that plane 

 from the bands issuing from the actual surface of the diatom. 



To fix our ideas, we might take Fig. 6 and cover up with a, 

 piece of white paper everything below the line A B. If now we 

 prolonged all the rays above this line downwards, the resulting 

 configuration would be quite different to the pattern covered up. 

 And yet it is the former and not the latter which would correspond 

 to the image observed in the microscope when racked down to 

 focus below the plane of A B. And if racked up to focus on a 

 plane above A B, as for example C D, light and darkness would 

 be seen as indicated in Fig. 6 in the plane of C D, which varies 

 greatly from the distribution of light and darkness in the 

 plane A B. 



This brings us to a very curious matter. Seeing that the 

 only planes which can really be seen are the upper surface of 

 the diatom or planes above it, it would seem natural that we 

 should and ought to focus our objective on the upper surface 

 plane exactly. But as a matter of fact my experiments so far 

 have led to the conclusion that we focus slightly below that plane, 

 and furthermore that the image we thereby get is actually a 

 truer image of the surface plane than if we focussed exactly 



